Energy dynamics in buildings are inherently stochastic in nature due to random fluctuations from various factors such as heat gain (including the solar) and ambient temperature. This paper proposes a theoretical framework for stochastic modeling of building thermal dynamics as well as its analytical solution strategies. Both the external temperature and the heat gain are modeled as stochastic processes, composed of a periodic (daily) mean-value function and a zero-mean deviation process obtained as the output process of a unit Gaussian white noise passing through a rational filter. Based on the measured climate data, the indicated mean-value functions and rational filters have been identified for different months of a year. Stochastic differential equations in the state vector form driven by white noise processes have been established, and analytical solutions for the mean-value function and covariance matrix of the state vector are obtained. This framework would allow a simple and efficient way to carry out predictions and parametric studies on energy dynamics of buildings with random and uncertain climate effects. It would also provide a basis for the robust design of energy efficient buildings with predictive controllers.

References

References
1.
Muehleisen
,
R. T.
,
Heo
,
Y.
,
Graziano
,
D. J.
, and
Guzowski
,
L. B.
,
2013
, “
Stochastic Energy Simulation for Risk Analysis of Energy Retrofits
,” Architectural Engineering Conference (
AEI
) 2013: Building Solutions for Architectural Engineering, American Society of Civil Engineers, Reston, VA, pp.
902
911
.
2.
Heo
,
Y.
,
Choudhary
,
R.
, and
Augenbroe
,
G.
,
2012
, “
Calibration of Building Energy Models for Retrofit Analysis Under Uncertainty
,”
Energy Build.
,
47
, pp.
550
560
.
3.
Andersen
,
K. K.
,
Madsen
,
H.
, and
Hansen
,
L. H.
,
2000
, “
Modelling the Heat Dynamics of a Building Using Stochastic Differential Equations
,”
Energy Build.
,
31
(
1
), pp.
13
24
.
4.
Ahuja
,
S.
, and
Peleš
,
S.
,
2013
, “
Building Energy Models: Quantifying Uncertainties Due to Stochastic Processes
,”
52nd IEEE Conference on Decision and Control
(
CDC
), Firenze, Italy, Dec. 10–13, pp.
4814
4820
.
5.
Sun
,
K.
,
Yan
,
D.
,
Hong
,
T.
, and
Guo
,
S.
,
2014
, “
Stochastic Modeling of Overtime Occupancy and Its Application in Building Energy Simulation and Calibration
,”
Build. Environ.
,
79
, pp.
1
12
.
6.
Virote
,
J.
, and
Neves-Silva
,
R.
,
2012
, “
Stochastic Models for Building Energy Prediction Based on Occupant Behavior Assessment
,”
Energy Build.
,
53
, pp.
183
193
.
7.
Oldewurtel
,
F.
,
Parisio
,
A.
,
Jones
,
C.
,
Morari
,
M.
,
Gyalistras
,
D.
,
Gwerder
,
M.
,
Stauch
,
V.
,
Lehmann
,
B.
, and
Wirth
,
K.
,
2010
, “
Energy Efficient Building Climate Control Using Stochastic Model Predictive Control and Weather Predictions
,”
American Control Conference
(
ACC
), Baltimore, MD, June 30–July 2, pp. 5100–5105.
8.
Davenport
,
W. B.
, and
Root
,
W. L.
,
1958
,
An Introduction to the Theory of Random Signals and Noise
, Vol.
159
,
McGraw-Hill
,
New York
.
9.
Nielsen
,
S. R. K.
,
2007
,
Structural Dynamics: Linear Stochastic Dynamics
,
5th Ed.
,
Aalborg University Press
,
Aalborg, Denmark
.
10.
Zill
,
D. G.
, and
Wright
,
W. S.
,
2012
,
Differential Equations With Boundary-Value Problems
,
Cengage Learning
, Boston, MA.
11.
Mitchell
,
M.
,
1998
,
An Introduction to Genetic Algorithms
,
MIT Press
, Marylebone, London.
12.
Clough
,
R.
, and
Penzien
,
J.
,
1993
,
Dynamics of Structures
, McGraw-Hill, New York.
You do not currently have access to this content.